Extremal function for Moser–Trudinger type inequality with logarithmic weight
نویسندگان
چکیده
منابع مشابه
a cauchy-schwarz type inequality for fuzzy integrals
نامساوی کوشی-شوارتز در حالت کلاسیک در فضای اندازه فازی برقرار نمی باشد اما با اعمال شرط هایی در مسئله مانند یکنوا بودن توابع و قرار گرفتن در بازه صفر ویک می توان دو نوع نامساوی کوشی-شوارتز را در فضای اندازه فازی اثبات نمود.
15 صفحه اولA more accurate half-discrete Hardy-Hilbert-type inequality with the logarithmic function
By means of the weight functions, the technique of real analysis and Hermite-Hadamard's inequality, a more accurate half-discrete Hardy-Hilbert-type inequality related to the kernel of logarithmic function and a best possible constant factor is given. Moreover, the equivalent forms, the operator expressions, the reverses and some particular cases are also considered.
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Let Ω be a bounded smooth domain in Rn, and u(x) a C1 function with compact support in Ω. Moser’s inequality states that there is a constant co, depending only on the dimension n, such that 1 |Ω| ∫ Ω e nω 1 n−1 n−1 u n n−1 dx ≤ co, where |Ω| is the Lebesgue measure of Ω, and ωn−1 the surface area of the unit ball in Rn. We prove in this paper that there are extremal functions for this inequalit...
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ژورنال
عنوان ژورنال: Nonlinear Analysis: Theory, Methods & Applications
سال: 2016
ISSN: 0362-546X
DOI: 10.1016/j.na.2016.01.024